We study the spin dynamics of individual black holes in a binary system .
In particular we focus on the polar precession of spins and the possibility of a complete flip of spins with respect to the orbital plane .
We perform a full numerical simulation that displays these characteristics .
We evolve equal mass binary spinning black holes for t = 20 , 000 M from an initial proper separation of d = 25 M down to merger after 48.5 orbits .
We compute the gravitational radiation from this system and compare it to 3.5 post-Newtonian generated waveforms finding close agreement .
We then further use 3.5 post-Newtonian evolutions to show the extension of this spin flip-flop phenomenon to unequal mass binaries .
We also provide analytic expressions to approximate the maximum flip-flop angle and frequency in terms of the binary spins and mass ratio parameters at a given orbital radius .
Finally we discuss the effect this spin flip-flop would have on accreting matter and other potential observational effects .